A Comparison of a Passive and Variable-Damping …agrosy.informatik.uni-kl.de/fileadmin/Literatur/Zhao13a.pdfApril 5, 2013 11:30 WSPC - Proceedings Trim Size: 9in x 6in passive_damping_prosthesis_FINAL

April 5, 2013 11:30 WSPC - Proceedings Trim Size: 9in x 6in passive˙damping˙prosthesis˙FINAL

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A Comparison of a Passive and Variable-Damping Controlled

Leg Prosthesis in a Simulated Environment

JIE ZHAO∗, KARSTEN BERNS∗, ROBERTO DE SOUZA BAPTISTA† and

ANTONIO PADILHA L. BO†∗Robotics Research Lab, University of Kaiserslautern,

Kaiserslautern, 67655, Germany∗E-mail: {zhao,berns}@informatik.uni-kl.de

†Automation and Robotics Laboratory, Unversity of Brasılia,

Brasılia, Brazil

This paper presents two control methods for a leg prosthesis: a passive basedand a variable-damping based. First, the concept of the mechanical design for

the leg prosthesis is described. A simulated environment is used to compare the

two control methods. The joint setup and its control scheme, in which a passiveor a variable-damping control can be easily implemented, are introduced for

the prosthetic leg in the simulated environment. Intelligent prosthesis require a

specific adjustment for each gait phase based on kinematic events of knee andankle joints along a gait cycle. A feasible damping profile is generated based

on kinematic and dynamical data of the knee joint along a gait cycle. This

data set was extracted from a simulated biped which is 1.8 m in height and76 kg in weight with 21 degrees of freedom during normal walking. The data

show that the damping profile is critical between the toe-off and heel contact

events. Tests using the simulated biped with the passive and the variable-damping controlled leg prosthesis during walking enables the comparison of

both control approaches.

Keywords: Leg prosthesis; Variable-damping control; Passive control; Roughterrain

Introduction

Amputations of lower limbs, which can occur due to trauma, infections

or other diseases, significantly decreases a person’s quality of life. Among

all basic locomotion affected walking is critical when compared to other

movements. This paper addresses the use of new tools in the development

of control strategies for artificial legs and presents a comparison between

two distinctive control methods, since its merits and drawbacks are still not


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clear. In the next sections, we start by describing the mechanical design of

ongoing leg prosthesis, its working principles and hardware setups. Based on

the mechanical setup, a passive control scheme for one joint will be briefly

introduced. Next, by parsing captured kinematic and dynamical data from

an existed simulated biped, a variable-damping controller is developed for

the leg prosthesis. We test both controllers on a simulated human with a leg

prosthesis and demonstrate their performances. Results demonstrate both

merits and drawbacks of each control method.

Mechanical Design of Leg Prosthesis

The knee module of the ongoing leg prosthesis project is a polycentric

knee mechanism with adjustable damping ratios. The main advantages of a

polycentric mechanism is a combination of stability at full extension, i.e. in

stance phase of gait, and better foot clearance in the swing phase of gait.1,2

As in various polycentric knee designs, our polycentric mechanism is based

on a four bar linkage system.3 A magnetorheological piston is integrated

to the prosthetic knee to provide damping adjustment of the mechanism.

Magnetorheological fluids alter its viscosity in the presence of a magnetic

field. A piston, or damper, filled with this type of fluid provides a continu-

ously variable damping force controlled by a desired input.4 In our project

we used a commercially available magnetorheological piston from Lord Cor-

poration. In this device, the magnetic field through the magnetorheological

fluid is induced by an electric current, which is the control input to adjust

the damping coefficient of the system. The prosthetic knee module proto-

type is currently in the finishing phase of production as shown in Fig. 1.

The goal of this project is to investigate different control strategies taking

into account human in the loop for above the knee amputees.

Fig. 1. Mechanical configuration of leg prosthesis in a simulated biped and prototype.


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Joint Setup and Control

The main feature of the joint setup is constant stiffness and damping, which

makes the joint compliant. Each joint consists of a parallel elastic element

and damper, except for prosthetic knee joint that has an additional variable-

damping control. Figure 2 presents the torque computation applied to im-

plement a constrained rotational movement of the prosthetic knee and the

passive joints at the ankle. Given the constant equilibrium point θ0 of the

Fig. 2. A variable-damping controlled knee joint. Other two passive joints don’t containelements inside dashed rectangle.

spring and the actual joint angle θ, the resulting torque is computed as

τspring = sgn (θ0 − θ) ·Kspring · (θ0 − θ)2 . (1)

The combined torque for the joint can be computed as

τ = τspring − τdamping − τk, (2)

with Kspring being the spring stiffness. Constant damping at each joint

is represented by the torque τdamping which is proportional to the joint’s

angular velocity while τk represents the torque generated by the variable-

damping controller at the knee joint if it is activated. Thus, for passive


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joints the combined torque should not include the last part of Eq. (2) , i.e.

τk.

Computation of Damping Coefficient at Knee Joint

Kinematic data of the knee joint along gait cycle was obtained simulating a

biped in a dynamic environmenta within the scenario of flat ground walking,

as shown in Fig. 3. The power consumption profile at the knee joint after

toe-off and before heel strike generally has negative magnitude. Associating

this feature to the physical damper, the knee can be modeled as a variable-

damper in this phase.

Fig. 3. Knee angle, velocity, torque and power along gait cycle.

The effective damping variable Bk is the ratio between the knee torque

τ and knee velocity θk. By using the data set illustrated in Fig. 3, the

damping coefficient can be directly calculated, as shown in Fig. 4.

According to Fig. 4, the damping coefficient can be characterized as a

function of knee angle:

Bk(θk) =

Bklow+Bkup

−Bklow

θkup− θklow

· (θk − θklow) , if θk > θklow

∞, otherwise(3)

In Eq. (3) θklowand θkup

represent a range in which knee joint can be mod-

elled as a variable damper whereas Bklowand Bkup indicate the damping

aThe detailed control architecture, i.e. biologically inspired control of a dynamicallywalking bipedal robot can be found in5


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Fig. 4. Knee damping coefficient along the knee angle during gait cycle.

coefficient at θklowand θkup , respectively.

Simulation Results

The variable-damping controlled leg prosthesis consists of one knee joint

and ankle joints in both sagittal and frontal plane. Except for the variable-

damping controlled knee joint, others joints are passive elements with fixed

stiffness and damping. A sliding joint is placed between top of the amputee’s

stump and the knee joint, whereas another is situated between knee and

ankle joint. Those two sliding joints, which are shown in Fig. 1, provide a

constant stiffness and lock mechanism that is used to lock knee angle during

late swing phase and stance phase.

Fig. 5. A simulated biped with a left prosthetic leg.

Meanwhile, the mechanically passive prosthesis consists of three passive

joints, e.g. knee joint, ankle joint in sagittal and frontal plane. The stiffness


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and damping ratio for each joint are predefined and can not be adjusted

during the walking phase as shown in Fig. 2.

Walking on the Even Ground

We first simulated the normal walking at a speed of 1.21 m/s on an even

platform without the presence of external disturbances. The results allow

a detailed evaluation of the calculated damping coefficient for the variable-

damping controlled leg prosthesis and the capability of the passive leg pros-

thesis.

Fig. 6. Joint angles and torques over the course of gait cycle. The solid lines in (a) and(c) represent mean values of passive prosthesis joints over 10 steps of normal walking,

whereas those in (b) and (d) show mean values of variable damping controlled prosthesis.The dashed lines mark the minimum and maximum values. The vertical dashed linedenotes the transition from stance to swing.

The kinetic data set of both types of prosthesis in this walking scenario is

illustrated in Fig. 6. Figures 6 (a) and (b) show the joint angles of passive

and variable-damping controlled prosthesis respectively. One can observe

that the courses of the kinematic data of the passive controlled joints are

actually more stable during gait cycle. Those curves present nearly similar

course during the gait cycle, which means that the choice of the damping

constant for passive prosthesis is also proper. The joint torques of passive

and variable-damping controlled prosthesis are shown in Fig. 6 (c) and

(d), respectively. The courses of torque generated in the passive joints have

nearly similar profiles as those in variable-damping controlled prosthesis


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which means they have almost the same performance on energy consump-

tion. However, while the variable-damping controlled prosthesis requires

extra mounting of electronic devices and thus more energy consumption,

the variable-damping controlled prosthesis exhibits no advantage in this

aspect.

Walking on the Rough Terrain

We have also tested walking in scenario of an uneven terrain with the un-

evenness up to about 3.3 mm. Simulation results show that the variable

damping controlled prosthesis is more adaptable to unknown rough terrain

than the passive prosthesis. Figures 7 (a) and (b) show the joints angles of

passive and variable-damping controlled prosthesis individually. The vari-

ances of joint angles of passive controlled prosthesis are clearly larger than

those in variable-damping controlled prosthesis. The joint torques of pas-

sive and variable-damping controlled prosthesis are shown in Fig. 7 (c) and

(d), respectively. The curves representing the passive controlled prosthesis

show greater dynamic variations of joint angles along a gait cycle, which

means more energy is required for keeping stability.

Fig. 7. Joint angles and torques of passive and variable-damping controlled prosthesisof amputees along gait cycle.

Table 1 exhibits standard deviations of the joints in prosthetic legs in

walking scenarios of flat ground and uneven terrain respectively. All joint

variables are captured from experiment of 10 gaits. One can observe that

the passive controlled prosthesis shows more deviations than the variable-


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damping controlled one. Also, walking on the uneven terrain introduces

more deviations on each joint due to unevenness of terrain. This result gives

us a clue that using variable-damping controlled prosthesis will improve the

stability of walking on unknown rough terrain compared to the passive one.

JointFlat Ground Uneven Terrain

passive variable-damping passive variable-damping

Hip Y 1.30◦ 1.24◦ 1.52◦ 1.26◦

Knee Y 1.50◦ 1.34◦ 1.88◦ 1.44◦

Ankle Y 1.50◦ 1.40◦ 1.78◦ 1.44◦

Ankle X 1.32◦ 1.26◦ 1.57◦ 1.30◦

Conclusion and Future Works

In this paper we described the development of a variable damping controlled

for a lower leg prosthesis using a simulated environment. We then pre-

sented a comparison between a passive controlled and a variable-damping

controlled prosthesis in different walking scenarios. Simulation results show

that there is no obvious difference between two approaches on flat ground

walking, but the variable-damping controlled prosthesis may need more

energy due to extra electrical instrumentation. On the other hand, the

variable-damping controlled prosthesis is more stable than the passive con-

trolled prosthesis on rough terrain walking.

Acknowledgments

The authors thank CAPESb and DAADc for the financial support.

References

1. M. P. Greene, “Four Bar Linkage Knee Analysis”, Orthotics Prosthetics,1983.

2. S. Pfeifer, et al., “An actuated transfemoral prosthesis with optimized poly-centric knee joint”, BioRob, 2012.

3. P. Tang, et al., “Let them walk! Current prosthesis options for leg and footamputees”, J. American College of Surgeons, 2008.

4. F. Li, et al., “The modeling research of Magnetorheological Damper in ad-vanced intelligent prosthesis”, CCDC, 2009.

5. T. Luksch, K. Berns, “Control of Bipedal Walking Exploiting Postural Re-flexes and Passive Dynamics”, ICABB, 2010.

bhttp://www.capes.gov.br/chttps://www.daad.de

Documents

A Comparison of a Passive and Variable-Damping …agrosy.informatik.uni-kl.de/fileadmin/Literatur/Zhao13a.pdfApril 5, 2013 11:30 WSPC - Proceedings Trim Size: 9in x 6in passive_damping_prosthesis_FINAL